Extended depth of field optical systems

ABSTRACT

A system for increasing the depth of field and decreasing the wavelength sensitivity and the effects of misfocus-producing aberrations of the lens of an incoherent optical system incorporates a special purpose optical mask into the incoherent system. The optical mask has been designed to cause the optical transfer function to remain essentially constant within some range from the in-focus position. Signal processing of the resulting intermediate image undoes the optical transfer modifying effects of the mask, resulting in an in-focus image over an increased depth of field. Generally the mask is placed at a principal plane or the image of a principal plane of the optical system. Preferably, the mask modifies only phase and not amplitude of light. The mask may be used to increase the useful range of passive ranging systems.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation of commonly owned andcopending U.S. patent application Ser. No. 09/070,969, filed on May 1,1998, which is a continuation-in-part of U.S. patent application Ser.No. 08/823,894 filed on Mar. 17, 1997, now U.S. Pat. No. 5,748,371,which is a continuation of application Ser. No. 08/384,257, filed Feb.3, 1995, now abandoned. U.S. Pat. No. 5,521,695, issued May 28, 1996 andentitled “Range Estimation Apparatus and Method,” is incorporated hereinby reference.

[0002] This invention was made with Government support awarded by theNational Science Foundation and the Office of Naval Research. TheGovernment has certain rights in this invention.

BACKGROUND OF THE INVENTION

[0003] 1. Field of the Invention

[0004] This invention relates to apparatus and methods for increasingthe depth of field and decreasing the wavelength sensitivity ofincoherent optical systems. This invention is particularly useful forincreasing the useful range of passive ranging systems. The sametechniques are applicable to passive acoustical and electromagneticranging systems.

[0005] 2. Description of the Prior Art

[0006] Improving the depth of field of optical systems has long been agoal of those working with imaging systems. A need remains in the artfor a simple imaging system, with one or only a few lenses, which nonethe less provides greatly expanded depth of field focusing. Depth offield refers to the depth in the scene being imaged. Depth of focusrefers to the depth in the image recording system.

[0007] A drawback of simple optical systems is that the images formedwith red light focus in a different plane from the images formed withblue or green light. There is only a narrow band of wavelengths in focusat one plane; the other wavelengths are out of focus. This is calledchromatic aberration. Currently, extending the band of wavelengths thatform an in-focus image is accomplished by using two or more lenses withdifferent indices of refraction to form what is called an achromaticlens. If it were possible to extend the depth of field of the system,the regions would extended where each wavelength forms an in-focusimage. If these regions can be made to overlap the system, after digitalprocessing, can produce (for example) a high resolution image at thethree different color bands of a television camera. The extended depthof focus system can, of course, be combined with an achromatic lens toprovide even better performance.

[0008] There are several other aberrations that result in misfocus.Astigmatism, for example, occurs when vertical lines and horizontallines focus in different planes. Spherical aberration occurs when radialzones of the lens focus at different planes. Field curvature occurs whenoff-axis field points focus on a curved surface. And temperaturedependent focus occurs when changes in ambient temperature effect thelens, shifting the best focus position. Each of these aberrations istraditionally compensated for by the use of additional lens elements.

[0009] The effects of these aberrations that causes a misfocus arereduced by the extended depth of imaging system. A larger depth of fieldgives the lens designer greater flexibility in balancing theaberrations.

[0010] The use of optical masks to improve image quality is also apopular field of exploration. For example, “Improvement in the OTF of aDefocussed Optical System Through the Use of Shaded Apertures”, by M.Mino and Y. Okano, Applied Optics, Vol. 10 No. 10, October 1971,discusses decreasing the amplitude transmittance gradually from thecenter of a pupil towards its rim to produce a slightly better image.“High Focal Depth By Apodization and Digital Restoration” by J.Ojeda-Castaneda et al, Applied Optics, Vol. 27 No. 12, June 1988,discusses the use of an iterative digital restoration algorithm toimprove the optical transfer function of a previously apodized opticalsystem. “Zone Plate for Arbitrarily High Focal Depth” by J.Ojeda-Castaneda et al, Applied Optics, Vol. 29 No. 7, March 1990,discusses use of a zone plate as an apodizer to increase focal depth.

[0011] All of these inventors, as well as all of the others in thefield, are attempting to do the impossible: achieve the point spreadfunction of a standard, in-focus optical system along with a large depthof field by purely optical means. When digital processing has beenemployed, it has been used to try to slightly clean up and sharpen animage after the fact.

SUMMARY OF THE INVENTION

[0012] The systems described herein give in-focus resolution over theentire region of the extended depth of focus. Thus it is especiallyuseful for compensating for misfocus aberrations, astigmatism, fieldcurvature, chromatic aberration, and temperature-dependent focus shifts.

[0013] An object of the present invention is to increase depth of fieldin an incoherent optical imaging system by adding a special purposeoptical mask to the system that has been designed to make it possiblefor digital processing to produce an image with in-focus resolution overa large range of misfocus by digitally processing the resultingintermediate image. The mask causes the optical transfer function toremain essentially constant within some range away from the in-focusposition. The digital processing undoes the optical transfer functionmodifying effects of the mask, resulting in the high resolution of anin-focus image over an increased depth of field.

[0014] A general incoherent optical system includes a lens for focusinglight from an object into an intermediate image, and means for storingthe image, such as film, a video camera, or a Charge Coupled Device(CCD) or the like. The depth of field of such an optical system isincreased by inserting an optical mask between the object and the CCD.The mask modifies the optical transfer function of the system such thatthe optical transfer function is substantially insensitive to thedistance between the object and the lens, over some range of distances.Depth of field post-processing is done on the stored image to restorethe image by reversing the optical transfer alteration accomplished bythe mask. For example, the post-processing means implements a filterwhich is the inverse of the alteration of the optical transfer functionaccomplished by the mask.

[0015] In general, the mask is located either at or near the aperturestop of the optical system or an image of the aperture stop. Generally,the mask is placed in a location of the optical system such that theresulting system can be approximated by a linear system. Placing themask at the aperture stop or an image of the aperture stop may have thisresult. Preferably, the mask is a phase mask that alters the phase whilemaintaining the amplitude of the light. For example, the mask could be acubic phase modulation mask.

[0016] The mask may be utilized in a wide field of view single lensoptical system, or in combination with a self focusing fiber or lens,rather than a standard lens.

[0017] A mask for extending the depth of field of an optical system maybe constructed by examining the ambiguity functions of several candidatemask functions to determine which particular mask function has anoptical transfer function which is closest to constant over a range ofobject distances and manufacturing a mask having the mask function ofthat particular candidate. The function of the mask may be divided amongtwo masks situated at different locations in the system.

[0018] A second object of the invention is to increase the useful rangeof passive ranging systems. To accomplish this object, the mask modifiesthe optical transfer function to be object distance insensitive asabove, and also encodes distance information into the image by modifyingthe optical system such that the optical transfer function containszeroes as a function of object range. Ranging post-processing meansconnected to the depth of field post-processing means decodes thedistance information encoded into the image and from the distanceinformation computes the range to various points within the object. Forexample, the mask could be a combined cubic phase modulation and linearphase modulation mask.

[0019] A third object of this invention is to extend the band ofwavelengths (colors) that form an in-focus image. By extending the depthof field of the system, the regions are extended where each wavelengthforms an in-focus image. These regions can be made to overlap and thesystem, after digital processing, can produce a high resolution image atthe three different color bands.

[0020] A fourth object of this invention is to extend the depth of fieldof imaging system s which include elements whose optical properties varywith temperature, or elements which are particularly prone to chromaticaberration.

[0021] A fifth object of this invention is to extend the depth of fieldof imaging system s to minimize the effects of misfocus aberrations likespherical aberration, astigmatism, and field curvature. By extending thedepth of field the misfocus aberration s can have overlapping regions ofbest focus. After digital processing, can produce images that minimizethe effects of the misfocus aberrations.

[0022] A sixth object of this invention is to physically join the maskfor extending depth of field with other optical elements, in order toincrease the depth of field of the imaging system without adding anotheroptical element.

[0023] Those having normal skill in the art will recognize the foregoingand other objects, features, advantages and applications of the presentinvention from the following more detailed description of the preferredembodiments as illustrated in the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0024]FIG. 1 shows a standard prior art imaging system.

[0025]FIG. 2 shows an Extended Depth of Field (EDF) imaging system inaccordance with the present invention.

[0026]FIG. 3 shows a mask profile for a Cubic-PM (C-PM) mask used inFIG. 2.

[0027]FIG. 4 shows the ambiguity function of the standard system of FIG.1.

[0028]FIG. 5 shows a top view of the ambiguity function of FIG. 4.

[0029]FIG. 6 shows the OTF for the standard FIG. 1 system with nomisfocus.

[0030]FIG. 7 shows the OTF for the standard FIG. 1 system with mildmisfocus.

[0031]FIG. 8 shows the Optical Transfer Function for the standard FIG. 1system with large misfocus.

[0032]FIG. 9 shows the ambiguity function of the C-PM mask of FIG. 3.

[0033]FIG. 10 shows the OTF of the extended depth of field system ofFIG. 2, with the C-PM mask of FIG. 3, with no misfocus and beforedigital processing.

[0034]FIG. 11 shows the OTF of the C-PM system of FIG. 2 with nomisfocus, after processing.

[0035]FIG. 12 shows the OTF of the C-PM system of FIG. 2 with mildmisfocus (before processing).

[0036]FIG. 13 shows the OTF of the C-PM system of FIG. 2 with mildmisfocus (after processing).

[0037]FIG. 14 shows the. OTF of the C-PM system of FIG. 2 with largemisfocus (before processing).

[0038]FIG. 15 shows the OTF of the C-PM system of FIG. 2 with largemisfocus (after processing).

[0039]FIG. 16 shows a plot of the Full Width at Half Maximum (FWHM) ofthe point spread function (PSF) as misfocus increases, for the standardsystem of FIG. 1 and the C-PM EDF system of FIG. 2.

[0040]FIG. 17 shows the PSF of the standard imaging system of FIG. 1with no misfocus.

[0041]FIG. 18 shows the PSF of the standard system of FIG. 1 with mildmisfocus.

[0042]FIG. 19 shows the PSF of the standard system of FIG. 1 with largemisfocus.

[0043]FIG. 20 shows the PSF of the C-PM system of FIG. 2 with nomisfocus, before digital processing.

[0044]FIG. 21 shows the PSF of the C-PM system of FIG. 2 with nomisfocus after processing.

[0045]FIG. 22 shows the PSF of the C-PM system of FIG. 2 with smallmisfocus after processing.

[0046]FIG. 23 shows the PSF of the C-PM system of FIG. 2 with largemisfocus after processing.

[0047]FIG. 24 shows a spoke image from the standard system of FIG. 1with no misfocus.

[0048]FIG. 25 shows a spoke image from the standard system of FIG. 1,with mild misfocus.

[0049]FIG. 26 shows a spoke image from the standard FIG. 1 system, withlarge misfocus.

[0050]FIG. 27 shows a spoke image from the FIG. 2 C-PM system with nomisfocus (before processing).

[0051]FIG. 28 shows a spoke image from the FIG. 2 C-PM system with nomisfocus (after processing).

[0052]FIG. 29 shows a spoke image from the FIG. 2 C-PM system with mildmisfocus (after processing).

[0053]FIG. 30 shows a spoke image from the FIG. 2 C-PM system with largemisfocus (after processing).

[0054]FIG. 31 shows an imaging system according to the present inventionwhich combines extended depth of field capability with passive ranging.

[0055]FIG. 32 shows a phase mask for passive ranging.

[0056]FIG. 33 shows a phase mask for extended depth of field and passiveranging, for use in the device of FIG. 31.

[0057]FIG. 34 shows the point spread function of the FIG. 31 embodimentwith no misfocus.

[0058]FIG. 35 shows the point spread function of the FIG. 31 embodimentwith large positive misfocus.

[0059]FIG. 36 shows the point spread function of the FIG. 31 embodimentwith large negative misfocus.

[0060]FIG. 37 shows the point spread function of the FIG. 31 embodimentwith no extended depth of field capability and no misfocus.

[0061]FIG. 38 shows the optical transfer function of the FIG. 31embodiment with no extended depth of field capability and with largepositive misfocus.

[0062]FIG. 39 shows the optical transfer function of the FIG. 31embodiment with no extended depth of field capability and with largenegative misfocus.

[0063]FIG. 40 shows the optical transfer function of the extended depthof field passive ranging system of FIG. 31 with a small amount ofmisfocus.

[0064]FIG. 41 shows the optical transfer function of a passive rangingsystem without extended depth of field capability and with a smallamount of misfocus.

[0065]FIG. 42 shows an EDF imaging system similar to that of FIG. 2,with plastic optical elements used in place of the lens of FIG. 2.

[0066]FIG. 43 shows an EDF imaging system similar to that of FIG. 2,with an infrared lens used in place of the lens of FIG. 2.

[0067]FIG. 44 shows a color filter joined with the EDF mask of FIG. 3.

[0068]FIG. 45 shows a combined lens/EDF mask according to the presentinvention.

[0069]FIG. 46 shows a combined diffractive grating/EDF mask according tothe present invention.

[0070]FIG. 47 shows and EDF optical system similar to that of FIG. 2,the lens having misfocus aberrations.

[0071]FIG. 48 shows an EDF optical system utilizing two masks indifferent locations in the system which combine to perform the EDFfunction, according to the present invention.

[0072]FIG. 49 shows an EDF imaging system similar to that of FIG. 2,with a self focusing fiber used in place of the lens of FIG. 2.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0073]FIG. 1 (prior art) shows a standard optical imaging system. Object15 is imaged through lens 25 onto Charge Coupled Device (CCD) 30. Such asystem creates a sharp, in-focus image at CCD 30 only if object 15 islocated at or very close to the in-focus object plane. If the distancefrom the back principal plane of lens 25 to CCD 30 is d_(i), and focallength of lens 25 is f, the distance, d₀, from the front principal planeof lens 25 to object 15 must be chosen such that:${\frac{1}{d_{o}} + \frac{1}{d_{i}} - \frac{1}{f}} = 0$

[0074] in order for the image at CCD 30 to be in-focus. The depth offield of an optical system is the distance the object can move away fromthe in-focus distance and still have the image be in focus. For a simplesystem like FIG. 1, the depth of field is very small.

[0075]FIG. 2 shows the interaction and operation of a multi-componentextended depth of field system in accordance with the invention. Object15 is imaged through optical mask 20 and lens 25 onto Charge CoupledDevice (CCD) system 30, and image post-processing is performed bydigital processing system 35. Those skilled in the art will appreciatethat any image recording and retrieval device could be used in place ofCCD system 30.

[0076] Mask 20 is composed of an optical material, such as glass orplastic film, having variations in opaqueness, thickness, or index ofrefraction. Mask 20 preferably is a phase mask, affecting only the phaseof the light transmitted and not its amplitude. This results in a highefficiency optical system. However, mask 20 may also be an amplitudemask or a combination of the two. Mask 20 is designed to alter anincoherent optical system in such a way that the system response to apoint object, or the Point Spread Function (PSF), is relativelyinsensitive to the distance of the point from the lens 25, over apredetermined range of object distances. Thus, the Optical TransferFunction (OTF) is also relatively insensitive to object distance overthis range. The resulting PSF is not itself a point. But, so long as theOTF does not contain any zeroes, image post processing may be used tocorrect the PSF and OTF such that the resulting PSF is nearly identicalto the in-focus response of a standard optical system over the entirepredetermined range of object distances.

[0077] The object of mask 20 is to modify the optical system in such away that the OTF of the FIG. 2 system is unaffected by the misfocusdistance over a particular range of object distances. In addition, theOTF should not contain zeroes, so that the effects of the mask (otherthan the increased depth of field) can be removed in post-processing.

[0078] A useful method of describing the optical mask function P(x)(P(x) is described in conjunction with FIGS. 3-30 below) is theambiguity function method. It happens that the OTF equation for anoptical system can be put in a form similar to the well known ambiguityfunction A(u,v). The ambiguity function is used in radar applicationsand has been extensively studied. The use and interpretation of theambiguity function for radar systems are completely different from theOTF, but the similarity in the form of the equations helps in workingwith the OTF. The ambiguity function is given by:

A(u,v)=∫{circumflex over (P)}(x+u/2){circumflex over (P)}*(x−u/2)e^(j2πxv) dx

[0079] where * denotes complex conjugate and where the mask functionP(x) is in normalized coordinates:${{\hat{P}(x)} = {\hat{P}( {x\frac{D}{2\pi}} )}},{{\hat{P}(x)} = {{0{x}} > \pi}}$

[0080] with D being the length of the one-dimensional mask. The aboveassumes two dimensional rectangularly separable masks for simplicity.Such systems theoretically can be completely described by a onedimensional mask.

[0081] As is known to those skilled in the art, given a general opticalmask function P(x), one can calculate the response of the incoherent OTFto any value of misfocus ψ by the equation:

H(u,ψ)=∫({circumflex over (P)}(x+u/2)e ^(j(x+u/2)) ² ^(ψ))({circumflexover (P)}*(x−u/2)e ^(−j(x−u/2)) ² ^(ψ))dx

[0082] The independent spatial parameter x and spatial frequencyparameter u are unitless because the equation has been normalized.

[0083] ψ is a normalized misfocus parameter dependent on the size oflens 25 and the focus state:$\psi = {\frac{L^{2}}{4{\pi\lambda}}( {\frac{1}{f} - \frac{1}{d_{0}} - \frac{1}{d_{i}}} )}$

[0084] Where L is the length of the lens, λ is the wavelength of thelight, f is the focal length of lens 25, d₀ is the distance from thefront principal plane to the object 15, and d_(i) is the distance fromthe rear principal plane to the image plane, located at CCD 30. Givenfixed optical system parameters, misfocus v is monotonically related toobject distance d₀.

[0085] It can be shown that the OTF and the ambiguity function arerelated as:

H(u,ψ)=A(u,uψ/π)

[0086] Therefore, the OTF is given by a radial slice through theambiguity function A(u,v) that pertains to the optical mask function{circumflex over (P)}(x). This radial line has a slope of ψ/π. Theprocess of finding the OTF from the ambiguity function is shown in FIGS.4-8. The power and utility of the relationship between the OTF and theambiguity function lie in the fact that a single two dimensionalfunction, A(u,v), which depends uniquely on the optical mask function{circumflex over (P)}(x), can represent the OTF for all values ofmisfocus. Without this tool, it would be necessary to calculate adifferent OTF function for each value of misfocus, making it difficultto determine whether the OTF is essentially constant over a range ofobject distances.

[0087] A general form of the one family of phase masks is Cubic phaseModulation (Cubic-PM). The general form is:

P(x,y)=exp(j(αx ³ +βy ³ +γx ² y+δxy ²)), |x|≦π, |y|≦π

[0088] Choice of the constants, α, β, γ, and δ allow phase functionsthat are rectangularly separable (with γ=δ=0) to systems whosemodulation transfer functions (MTF's) are circularly symmetric (α=β=α₀,γ=δ=−3α₀). For simplicity we will use the symmetric rectangularlyseparable form, which is given by:

P(x,y)=exp(jα(x ³ +y ³)), |x|≦π|y|≦π

[0089] Since this form is rectangularly separable, for most analysisonly its one dimensional component must be considered:

{circumflex over (P)}(x)=exp(jαx ³),|x|≦π

[0090] where α is a parameter used to adjust the depth of fieldincrease.

[0091]FIG. 3 shows the mask implementing this rectangularly separablecubic phase function. When α=0, the mask function is the standardrectangular function given by no mask or by a transparent mask. As theabsolute value of α increases, the depth of field increases. The imagecontrast before post-processing also decreases as a increases. This isbecause as α increases, the ambiguity function broadens, so that it isless sensitive to misfocus. But, since the total volume of the ambiguityfunction stays constant, the ambiguity function flattens out as itwidens.

[0092] For large enough α, the OTF of a system using a cubic PM mask canbe approximated by:${{H( {u,\psi} )} \approx {\sqrt{\frac{\pi}{3{{\alpha \quad u}}}}^{{- j}\frac{\alpha \quad u^{3}}{4}}}},{u \neq 0}$

 H(u,ψ)≈2,u=0

[0093] Appendix A gives the mathematics necessary to arrive at the aboveOTF function.

[0094] Thus, the cubic-PM mask is an example of a mask which modifiesthe optical system to have a near-constant OTF over a range of objectdistances. The particular range for which the OTF does not vary much isdependent of α. The range (and thus the depth of field) increases withα. However, the amount that depth of field can be increased ispractically limited by the fact that contrast decreases as a increases,and eventually contrast will go below the system noise.

[0095]FIGS. 4 through 30 compare and contrast the performance of thestandard imaging system of FIG. 1 and a preferred embodiment of theextended depth of field system of FIG. 2, which utilizes the C-PM maskof FIG. 3.

[0096] In the following description, the systems of FIG. 1 and FIG. 2are examined using three methods. First, the magnitude of the OTFs ofthe two systems are examined for various values of misfocus. Themagnitude of the OTF of a system does not completely describe thequality of the final image. Comparison of the ideal OTF (the standardsystem of FIG. 1 when in focus) with the OTF under other circumstancegives a qualitative feel for how good the system is.

[0097] Second, the PSFs of the two systems are compared. The full widthat half maximum amplitude of the PSFs gives a quantitative value forcomparing the two systems. Third, images of a spoke picture formed bythe two systems are compared. The spoke picture is easily recognizableand contains a large range of spatial frequencies. This comparison isquite accurate, although it is qualitative.

[0098]FIG. 4 shows the ambiguity function of the standard optical systemof FIG. 1. Most of the power is concentrated along the v=0 axis, makingthe system very sensitive to misfocus. FIG. 5 is the top view of FIG. 4.Large values of the ambiguity function are represented by dark shades inthis figure. The horizontal axis extends from −2π to 2π. As discussedabove, the projection of a radial line drawn through the ambiguityfunction with slope ψ/π determines the OTF for misfocus. This radialline is projected onto the spatial frequency u axis. For example, thedotted line on FIG. 5 was drawn with a slope of 1/(2π). This linecorresponds to the OTF of the standard system of FIG. 1 for a misfocusvalue of ψ=½. The magnitude of this OTF is shown in FIG. 7.

[0099]FIG. 6 shows the magnitude of the OTF of the standard system ofFIG. 1 with no misfocus. This plot corresponds to the radial line drawnhorizontally along the horizontal u axis in FIG. 5.

[0100]FIG. 7 shows the magnitude of the OTF for a relatively mildmisfocus value of ½. This OTF corresponds to the dotted line in FIG. 5.Even for a misfocus of ½, this OTF is dramatically different from theOTF of the in-focus system, shown in FIG. 6.

[0101]FIG. 8 shows the magnitude of the OTF for a rather large misfocusvalue of ψ=3. It bears very little resemblance to the in-focus OTF ofFIG. 6.

[0102]FIG. 9 shows the ambiguity function of the extended depth of fieldsystem of FIG. 2 utilizing the C-PM mask of FIG. 3 (the C-PM system).This ambiguity function is relatively flat, so that changes in misfocusproduce little change in the system OTF. α, defined on page 12, is setequal to three for this particular system, designated “the C-PM system”herein.

[0103]FIG. 10 shows the magnitude of the OTF of the C-PM system of FIG.2 before digital filtering is done. This OTF does not look much like theideal OTF of FIG. 6. However, the OTF of the entire C-PM EDF system(which includes filtering) shown in FIG. 11 is quite similar to FIG. 6.The high frequency ripples do not affect output image quality much, andcan be reduced in size by increasing a.

[0104]FIG. 12 shows the magnitude of the OTF of the C-PM system of FIG.2 with mild misfocus (ψ=½), before filtering. Again, this OTF doesn'tlook like FIG. 6. It does, however look like FIG. 10, the OTF for nomisfocus. Thus, the same filter produces the final OTF shown in FIG. 13,which does resemble FIG. 6.

[0105]FIG. 14 shows the magnitude of the OTF of THE C-PM system of FIG.2 with large misfocus (ψ=3), before filtering. FIG. 15 shows themagnitude of the OTF of the entire C-PM system. Notice that it is thefact that the OTFs before processing in all three cases (no misfocus,mild misfocus, and large misfocus) are almost the same that allows thesame post-processing, or filter, to restore the OTF to near ideal.

[0106] Note that while the OTF of the FIG. 2C-PM system is nearlyconstant for the three values of misfocus, it does not resemble theideal OTF of FIG. 10. Thus, it is desirable that the effect of the FIG.3 mask (other than the increased depth of field) be removed bypost-processing before a sharp image is obtained. The effect of the maskmay be removed in a variety of ways. In the preferred embodiment, thefunction implemented by post-processor (preferably a digital signalprocessing algorithm in a special purpose electronic chip, but alsopossible with a digital computer or an electronic or optical analogprocessor) is the inverse of the OTF (approximated as the function H(u),which is constant over ψ). Thus, the post-processor 35 must, in general,implement the function:$\sqrt{\frac{3{{\alpha \quad u}}}{\pi}}^{j\frac{\alpha \quad u^{3}}{4}}$

[0107] FIGS. 16-23 show the Point Spread Functions (PSFs) for thestandard system of FIG. 1 and the C-PM system of FIG. 2 for varyingamounts of misfocus. FIG. 16 shows a plot of normalized Full Width atHalf Maximum amplitude (FWHM) of the point spread functions versusmisfocus for the two systems. The FWHM barely changes for the FIG. 2C-PM system, but rises rapidly for the FIG. 1 standard system.

[0108]FIGS. 17, 18, and 19 show the PSFs associated with the FIG. 1standard system for misfocus values of 0, 0.5, and 3, (no misfocus, mildmisfocus, and large misfocus) respectively. The PSF changes dramaticallyeven for mild misfocus, and is entirely unacceptable for large misfocus.

[0109]FIG. 20 shows the PSF for the FIG. 2 C-PM system with no misfocus,before filtering (post-processing). It does not look at all like theideal PSF of FIG. 17, but again, the PSF after filtering, shown in FIG.21 does. The PSFs of the FIG. 2 C-PM system for mild misfocus is shownin FIG. 22, and the PSF for the FIG. 2 C-PM system with large misfocusis shown in FIG. 23. All three PSFs from the entire system are nearlyindistinguishable from each other and from FIG. 17.

[0110]FIG. 24 shows an image of a spoke picture formed by the FIG. 1standard system with no misfocus. FIG. 25 shows an image of the samepicture formed by the FIG. 1 standard system with mild misfocus. You canstill discern the spokes, but the high frequency central portion of thepicture is lost. FIG. 26 shows the FIG. 1 standard system image formedwith large misfocus. Almost no information is carried by the image.

[0111]FIG. 27 is the image of the spoke picture formed by the FIG. 2C-PM system, before digital processing. The image formed afterprocessing is shown in FIG. 28. The images formed by the complete FIG. 2system with mild and large misfocus are shown in FIGS. 29 and 30,respectively. Again, they are almost indistinguishable from each other,and from the ideal image of FIG. 24.

[0112]FIG. 31 shows an optical system according to the present inventionfor extended depth of field passive ranging. Passive ranging using anoptical mask is described in U.S. Pat. No. 5,521,596 entitled “RangeEstimation Apparatus and Method” by the present inventors, hereinincorporated by reference. U.S. Pat. No. 5,521,596 discusses systemscontaining range dependent null space, which is substantially similar tothe range dependent zeroes discussed below.

[0113] In FIG. 31, general lens system 40 has front principal plane (orfocal plane) 42 and back principal plane 43. Generally, optical mask 60is placed at or near one of the principal planes, but mask 60 may alsobe placed at the image of one of the principal planes, as shown in FIG.31. This allows beam splitter 45 to generate a clear image 50 of theobject (not shown). Lens 55 projects an image of back focal plane 43onto mask 60. Mask 60 is a combined extended depth of field and passiveranging mask. CCD 65 samples the image from mask 60. Digital filter 70is a fixed digital filter matched to the extended depth of fieldcomponent of mask 60. Filter 70 returns the PSF of the image to a pointas described above. Range estimator 75 estimates the range to variouspoints on the object (not shown) by estimating the period of therange-dependant nulls or zeroes.

[0114] Briefly, passive ranging is accomplished by modifying theincoherent optical system of FIG. 2 in such a way that range dependentzeroes are present in the Optical Transfer Function (OTF). Note that theOTF of the EDF system discussed above could not contain zeroes, becausethe zeroes cannot be removed by post filtering to restore the image. InFIG. 31, however, zeroes are added to encode the wavefront with rangeinformation. To find the range associated with small specific blocks ofthe image, the period of zeroes within a block is related to the rangeto the object imaged within the block. U.S. Pat. No. 5,521,596 primarilydiscusses amplitude masks, but phase masks can also produce an OTF withzeroes as a function of object range, and without loss of opticalenergy. Current passive ranging systems can only operate over a verylimited object depth, beyond which it becomes impossible to locate thezeroes, because the OTF main lobe is narrowed, and the ranging zeroesget lost in the OTF lobe zeroes. Extending the depth of field of apassive ranging system makes such a system much more useful.

[0115] Consider a general mask 60 for passive ranging describedmathematically as:${{P(x)} = {\sum\limits_{S = 0}^{S - 1}\quad {{\mu_{S}( {x - {sT}} )}^{j\quad {w_{s}{({x - {sT}})}}}}}},{{x} \leq {\pi/S}}$${\mu_{s}(x)} = {{0\quad {for}\quad {x}} > \frac{\pi}{s}}$

[0116] This mask is composed of S phase modulated elements μ_(s)(x) oflength T, where S·T=2π. Phase modulation of each segment is given by theexponential terms. If the above mask is a phase mask then the segmentsμ_(s)(x), s=0, 1, . . . ,s−1, satisfy |μ₅(x)|=1. A simple example ofthis type of mask is shown in FIG. 32. This is a two segment (S=2) phasemask where ω₀=−π/2, ω₁=π/2.

[0117]FIG. 32 shows an example of a phase passive ranging mask 80, whichcan be used as mask 60 of FIG. 31. This mask is called a Linear PhaseModulation (LPM) mask because each of the segments modulates phaselinearly. Mask 80 comprises two wedges or prisms 81 and 82 with reversedorientation. Without optional filter 85, the formed image is the sum ofthe left and right components. Optional filter 85 comprises two halves86 and 87, one under each wedge. Half 86 is orthogonal to half 87, inthe sense that light which passes through one half will not pass throughthe other. For example, the filters could be different colors (such asred and green, green and blue, or blue and red), or could be polarizedin perpendicular directions. The purpose of filter 85 is to allowsingle-lens stereograms to be produced. A stereogram is composed of twoimages that overlap, with the distance between the same point in eachimage being determined by the object range to that point.

[0118]FIG. 33 shows the optical mask function of a combined LPM passiveranging mask and Cubic-PM mask 60 of FIG. 31 which is suitable forpassive ranging over a large depth of field. This mask is described by:

P(x)=μ(x)e ^(jαx) ³ e ^(jω) ^(₀) ^(x)+μ(x−π)e ^(jα(x−π)) ³ e ^(jw) ^(₁)^((x−π)),

[0119] where μ(x)=1 for 0≦x≦π,

[0120] 0 otherwise

[0121] By using two segments for the LPM component of mask 60, two lobesof the PSF will be produced.

[0122] The PSF of the imaging system of FIG. 31, using a mask 60 havingthe FIG. 33 characteristics, with misfocus ψ=0 (no misfocus), is shownin FIG. 34. This system will be called the EDF/PR system, for extendeddepth of field/passive ranging. The PSF has two peaks because of the twosegments of mask 60.

[0123]FIG. 35 shows the PSF of the EDF/PR system with y=10. The factthat ψ is positive indicates that the object is on the far side of thein-focus plane from the lens. The two peaks of the PSF have moved closertogether. Thus, it can be seen that the misfocus (or distance fromin-focus plane) is related to the distance between the peaks of the PSF.The actual processing done by digital range estimator 75 is, of course,considerably more complicated, since an entire scene is received byestimator 75, and not just the image of a point source. This processingis described in detail in U.S. Pat. No. 5,521,596.

[0124]FIG. 36 shows the PSF of the EDF/PR system with ψ=−10. The factthat ψ is negative indicates that the object is nearer to the lens thanis the in-focus plane The two peaks of the PSF have moved farther apart.This allows estimator 75 to determine not only how far the object isfrom the in focus plane, but which direction.

[0125] It is important to note that while the distance between the peaksof the PSF varies with distance, the peaks themselves remain narrow andsharp because of the EDF portion of mask 60 combined with the operationof digital filter 70.

[0126]FIG. 37 shows the PSF of a system with an LPM mask 80 of FIG. 31,without the EDF portion, and with no misfocus. Since there is nomisfocus, FIG. 37 is very similar to FIG. 34. FIG. 38 shows the PSF ofmask 80 without EDF and with large positive misfocus (ψ=10). The peakshave moved together, as in FIG. 35. It would be very difficult, however,for any amount of digital processing to determine range from this PSFbecause the peaks are so broadened. FIG. 39 shows the PSF of mask 80with no EDF and large negative misfocus (ψ=−10). The peaks have movedapart, but it would be difficult to determine by how much because of thelarge amount of misfocus.

[0127] That is, FIG. 39 shows the PSF of the LPM system without extendeddepth of field capability and with large negative misfocus (ψ=−10). Thepeaks have moved further apart, but again it would be very difficult todetermine the location of the peaks.

[0128]FIG. 40 shows the optical transfer function of the combined EDFand LPM system shown in FIG. 31, with a small amount of misfocus (ψ=1).The envelope of the OTF is essentially the triangle of the perfectsystem (shown in FIG. 6). The function added to the OTF by the rangingportion of the mask of FIG. 33 includes range dependent zeroes, orminima. The digital processing looks for these zeroes to determine therange to different points in the object.

[0129]FIG. 41 shows the optical transfer function of the FIG. 31embodiment with no extended depth of field capability and small misfocus(ψ=1). The envelope has moved from being the ideal triangle (shown inFIG. 6) to having a narrowed central lobe with side lobes. It is stillpossible to distinguish the range dependent zeroes, but it is becomingmore difficult, because of the low value of the envelope between themain lobe and the side lobes. As the misfocus increases, the main lobenarrows and the envelope has low values over a larger area. Therange-dependant minima and zeroes tend to blend in with the envelopezeroes to the extent that digital processing 70, 75 cannot reliablydistinguish them.

[0130]FIG. 42 shows an optical system 100, similar to the imaging systemof FIG. 2, but utilizing plastic optical elements 106 and 108 in placeof lens 25. Optical elements 106, 108 are affixed using spacers 102,104, which are intended to retain elements 106, 108 at a fixed locationin the optical system, with a fixed spacing between elements 106, 108.All optical elements, and especially plastic elements, are subject tochanges in geometry as well as changes in index of refraction withvariations in temperature. For example, PMMA, a popular plastic foroptical elements, has an index of refraction that changes withtemperature 60 times faster than that of glass. In addition, spacers 102and 104 will change in dimension with temperature, growing slightlylonger as temperature increases. This causes elements 106, 108 to moveapart as temperature increases.

[0131] Thus, changes in temperature result in changes in the performanceof optical systems like 100. In particular, the image plane of anoptical system like 100 will move with temperature. EDF mask 20,combined with digital processing 35, increases the depth of field of thesystem 100, reducing the impact of this temperature effect. In FIG. 42,mask 210 is located between elements 102, 104, but mask 20 may also belocated elsewhere in the optical system.

[0132] EDF mask 20 (combined with processing 35) also reduces the impactof chromatic aberrations caused by elements 106, 108. Plastic opticalelements are especially prone to chromatic aberrations due to thelimited number of different plastics that have good optical properties.Common methods of reducing chromatic aberrations, such as combining twoelements having different indices of refraction, are usually notavailable. Thus, the increase of depth of field provided by the EDFelements 20, 35, is particularly important in systems including plasticelements.

[0133]FIG. 43 shows an infrared lens 112 used in place of lens 25 in theimaging system of FIG. 2. Dotted line 114 shows the dimensions of lens112 at an increased temperature. Infrared materials such as Germaniumare especially prone to thermal effects such as changes in dimension andchanges in index of refraction with changes in temperature. The changein index of refraction with temperature is 230 times that of glass. EDFfilter 20 and processing 35 increase the depth of field of opticalsystem 110, reducing the impact of these thermal effects.

[0134] Like plastic optical elements, infrared optical elements are moreprone to chromatic aberration than glass elements. It is especiallydifficult to reduce chromatic aberration in infrared elements, due tothe limited number of infrared materials available. Common methods ofreducing chromatic aberrations, such as combining two elements havingdifferent indices of refraction, are usually not available. Thus, theincrease in depth of field provided by the EDF elements is particularlyimportant in infrared systems.

[0135]FIG. 44 shows a color filter 118 joined with EDF mask 20. In someoptical systems it is desirable to process or image only one wavelengthof light, e.g. red light. In other systems a grey filter may be used. Insystems utilizing a color filter, EDF mask 120 may be affixed to thecolor filter or formed integrally with the color filter of a singlematerial, to form a single element.

[0136]FIG. 45 shows a combined lens/EDF mask 124 (the EDF mask is not toscale). This element could replace lens 25 and mask 20 of the imagingsystem of FIG. 2, for example. In this particular example, the mask andthe lens are formed integrally. A first surface 126 implements thefocusing function, and a second surface 128 also implements the EDF maskfunction. Those skilled in the art will appreciate that these twofunctions could be accomplished with a variety of mask shapes.

[0137]FIG. 46 shows a combined diffractive grating/EDF mask 130. Grating134 could be added to EDF mask 132 via an embossing process, forexample. Grating 134 may comprise a modulated grating, e.g. tocompensate for chromatic aberration, or it might comprise a diffractiveoptical element functioning as a lens or as an antialiasing filter.

[0138]FIG. 47 shows an EDF optical system similar to that of FIG. 2,wherein lens 142 exhibits misfocus aberrations. Misfocus aberrationsinclude astigmatism, which occurs when vertical and horizontal linesfocus in different planes, spherical aberration, which occurs whenradial zones of the lens focus at different planes, and field curvature,which occurs when off-axis field points focus on a curved surface. Mask20, in conjunction with post processing 35 extend the depth of field ofthe optical system, which reduces the effect of these misfocusaberrations.

[0139]FIG. 48 shows an optical system 150 utilizing two masks 152, 156in different locations in the system, which combine to perform the EDFmask function of mask 20. This might be useful to implement verticalvariations in mask 152 and horizontal variations in mask 156, forexample. In the particular example of FIG. 48, masks 152, 156 arearrayed on either side of lens 154. This assembly could replace lens 25and mask 20 in the imaging system of FIG. 2, for example.

[0140]FIG. 49 shows an optical imaging system like that of FIG. 2, withlens 25 replaced by a self focusing element 162. Element 162 focuseslight not by changes in the thickness of the optical material across thecross section of the element (such as the shape of a lens), but ratherby changes in the index of refraction of the material across the crosssection of the element.

[0141] While the exemplary preferred embodiments of the presentinvention are described herein with particularity, those having normalskill in the art will recognize various changes, modifications,additions and applications other than those specifically mentionedherein without departing from the spirit of this invention.

What is claimed is:
 1. A method for generating an optical image,comprising: forming an optical image with at least one optical elementwhile modifying wavefront phase such that there are no zeros insubsequent detected spatial frequencies of the optical image over anextended depth of focus that is larger than a depth of focus occurringwithout modifying wavefront phase.
 2. The method of claim 1, the step ofmodifying phase comprising utilizing an optical mask.
 3. The method ofclaim 2, further comprising the step of post-processing the opticalimage to remove effects induced by the optical mask, to render anelectronic image that is clearer over the extended depth of focus ascompared to an electronic image formed without the optical mask and overthe extended depth of focus.
 4. The method of claim 2, furthercomprising the step of post-processing the optical image to reduceeffects induced by the optical mask, to render an electronic image thatis clearer over the depth of focus as compared to an electronic imageformed without the optical mask and over the extended depth of focus. 5.The method of claim 1, further comprising the step of post-processingthe optical image to remove effects induced by the optical mask.
 6. Themethod of claim 1, further comprising the step of post-processing theoptical image to reduce effects induced by the optical mask.
 7. A systemfor forming an image, comprising: at least one lens and an optical maskthat cooperate to form an optical image, the optical mask modifyingwavefront phase such that there are no zeros in subsequent detectedspatial frequencies of the optical image over an extended depth of focuslarger than a depth of focus formed without the optical mask.
 8. Thesystem of claim 7, further comprising a detector for detecting theoptical image and a post-processor for processing the detected opticalimage to reverse blurring effects induced by the optical mask and toform an electronic image that is clearer over the extended depth offocus as compared to an electronic image formed without the optical maskand over the extended depth of focus.
 9. A system for forming an image,comprising: a lens and a phase mask that cooperate to form an opticalimage characterized by an optical transfer function that has no zeroswithin detected spatial frequencies of a detector over a larger depth offocus than without the phase mask.
 10. The system of claim 9, furthercomprising a detector that detects the optical image and means forpost-processing the detected optical image to generate an electronicimage that is clear over an extended depth of field.
 11. A system havinginsensitivity to misfocus, comprising: at least one lens and an opticalmask that cooperate to form an optical image, the optical mask modifyingwavefront phase such that there are no zeros in subsequent detectedspatial frequencies of the optical image over a range of misfocus beyond+/−pi/10.